Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24191 | −1.58527 | −0.792634 | − | 0.609698i | \(-0.791291\pi\) | ||||
−0.792634 | + | 0.609698i | \(0.791291\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.02615 | 1.51307 | ||||||||
\(5\) | −1.20404 | −0.538463 | −0.269231 | − | 0.963075i | \(-0.586770\pi\) | ||||
−0.269231 | + | 0.963075i | \(0.586770\pi\) | |||||||
\(6\) | −2.24191 | −0.915255 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.30052 | −0.813358 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.69935 | 0.853608 | ||||||||
\(11\) | 3.48348 | 1.05031 | 0.525154 | − | 0.851007i | \(-0.324008\pi\) | ||||
0.525154 | + | 0.851007i | \(0.324008\pi\) | |||||||
\(12\) | 3.02615 | 0.873573 | ||||||||
\(13\) | 3.78465 | 1.04967 | 0.524836 | − | 0.851203i | \(-0.324127\pi\) | ||||
0.524836 | + | 0.851203i | \(0.324127\pi\) | |||||||
\(14\) | 2.24191 | 0.599175 | ||||||||
\(15\) | −1.20404 | −0.310882 | ||||||||
\(16\) | −0.894732 | −0.223683 | ||||||||
\(17\) | 3.70393 | 0.898334 | 0.449167 | − | 0.893448i | \(-0.351721\pi\) | ||||
0.449167 | + | 0.893448i | \(0.351721\pi\) | |||||||
\(18\) | −2.24191 | −0.528422 | ||||||||
\(19\) | 6.98234 | 1.60186 | 0.800929 | − | 0.598759i | \(-0.204339\pi\) | ||||
0.800929 | + | 0.598759i | \(0.204339\pi\) | |||||||
\(20\) | −3.64360 | −0.814734 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −7.80963 | −1.66502 | ||||||||
\(23\) | 3.91380 | 0.816084 | 0.408042 | − | 0.912963i | \(-0.366212\pi\) | ||||
0.408042 | + | 0.912963i | \(0.366212\pi\) | |||||||
\(24\) | −2.30052 | −0.469592 | ||||||||
\(25\) | −3.55029 | −0.710058 | ||||||||
\(26\) | −8.48483 | −1.66401 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.02615 | −0.571888 | ||||||||
\(29\) | 8.03776 | 1.49258 | 0.746288 | − | 0.665624i | \(-0.231834\pi\) | ||||
0.746288 | + | 0.665624i | \(0.231834\pi\) | |||||||
\(30\) | 2.69935 | 0.492831 | ||||||||
\(31\) | 4.13048 | 0.741857 | 0.370928 | − | 0.928661i | \(-0.379040\pi\) | ||||
0.370928 | + | 0.928661i | \(0.379040\pi\) | |||||||
\(32\) | 6.60695 | 1.16796 | ||||||||
\(33\) | 3.48348 | 0.606396 | ||||||||
\(34\) | −8.30386 | −1.42410 | ||||||||
\(35\) | 1.20404 | 0.203520 | ||||||||
\(36\) | 3.02615 | 0.504358 | ||||||||
\(37\) | −6.15109 | −1.01123 | −0.505616 | − | 0.862758i | \(-0.668735\pi\) | ||||
−0.505616 | + | 0.862758i | \(0.668735\pi\) | |||||||
\(38\) | −15.6538 | −2.53937 | ||||||||
\(39\) | 3.78465 | 0.606029 | ||||||||
\(40\) | 2.76992 | 0.437963 | ||||||||
\(41\) | 11.3772 | 1.77681 | 0.888407 | − | 0.459056i | \(-0.151812\pi\) | ||||
0.888407 | + | 0.459056i | \(0.151812\pi\) | |||||||
\(42\) | 2.24191 | 0.345934 | ||||||||
\(43\) | −9.34313 | −1.42481 | −0.712407 | − | 0.701766i | \(-0.752395\pi\) | ||||
−0.712407 | + | 0.701766i | \(0.752395\pi\) | |||||||
\(44\) | 10.5415 | 1.58919 | ||||||||
\(45\) | −1.20404 | −0.179488 | ||||||||
\(46\) | −8.77437 | −1.29371 | ||||||||
\(47\) | −5.42356 | −0.791108 | −0.395554 | − | 0.918443i | \(-0.629447\pi\) | ||||
−0.395554 | + | 0.918443i | \(0.629447\pi\) | |||||||
\(48\) | −0.894732 | −0.129143 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.95941 | 1.12563 | ||||||||
\(51\) | 3.70393 | 0.518653 | ||||||||
\(52\) | 11.4529 | 1.58823 | ||||||||
\(53\) | 5.74006 | 0.788458 | 0.394229 | − | 0.919012i | \(-0.371012\pi\) | ||||
0.394229 | + | 0.919012i | \(0.371012\pi\) | |||||||
\(54\) | −2.24191 | −0.305085 | ||||||||
\(55\) | −4.19425 | −0.565552 | ||||||||
\(56\) | 2.30052 | 0.307420 | ||||||||
\(57\) | 6.98234 | 0.924833 | ||||||||
\(58\) | −18.0199 | −2.36613 | ||||||||
\(59\) | 1.34548 | 0.175167 | 0.0875833 | − | 0.996157i | \(-0.472086\pi\) | ||||
0.0875833 | + | 0.996157i | \(0.472086\pi\) | |||||||
\(60\) | −3.64360 | −0.470387 | ||||||||
\(61\) | 3.12982 | 0.400732 | 0.200366 | − | 0.979721i | \(-0.435787\pi\) | ||||
0.200366 | + | 0.979721i | \(0.435787\pi\) | |||||||
\(62\) | −9.26016 | −1.17604 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −13.0227 | −1.62784 | ||||||||
\(65\) | −4.55687 | −0.565210 | ||||||||
\(66\) | −7.80963 | −0.961300 | ||||||||
\(67\) | −5.24309 | −0.640546 | −0.320273 | − | 0.947325i | \(-0.603775\pi\) | ||||
−0.320273 | + | 0.947325i | \(0.603775\pi\) | |||||||
\(68\) | 11.2086 | 1.35925 | ||||||||
\(69\) | 3.91380 | 0.471166 | ||||||||
\(70\) | −2.69935 | −0.322633 | ||||||||
\(71\) | −9.77372 | −1.15993 | −0.579964 | − | 0.814642i | \(-0.696933\pi\) | ||||
−0.579964 | + | 0.814642i | \(0.696933\pi\) | |||||||
\(72\) | −2.30052 | −0.271119 | ||||||||
\(73\) | 5.34108 | 0.625126 | 0.312563 | − | 0.949897i | \(-0.398812\pi\) | ||||
0.312563 | + | 0.949897i | \(0.398812\pi\) | |||||||
\(74\) | 13.7902 | 1.60307 | ||||||||
\(75\) | −3.55029 | −0.409952 | ||||||||
\(76\) | 21.1296 | 2.42373 | ||||||||
\(77\) | −3.48348 | −0.396979 | ||||||||
\(78\) | −8.48483 | −0.960718 | ||||||||
\(79\) | −9.87463 | −1.11098 | −0.555491 | − | 0.831522i | \(-0.687470\pi\) | ||||
−0.555491 | + | 0.831522i | \(0.687470\pi\) | |||||||
\(80\) | 1.07729 | 0.120445 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −25.5065 | −2.81673 | ||||||||
\(83\) | −11.6734 | −1.28132 | −0.640659 | − | 0.767825i | \(-0.721339\pi\) | ||||
−0.640659 | + | 0.767825i | \(0.721339\pi\) | |||||||
\(84\) | −3.02615 | −0.330180 | ||||||||
\(85\) | −4.45968 | −0.483720 | ||||||||
\(86\) | 20.9464 | 2.25871 | ||||||||
\(87\) | 8.03776 | 0.861739 | ||||||||
\(88\) | −8.01383 | −0.854277 | ||||||||
\(89\) | 3.17892 | 0.336965 | 0.168483 | − | 0.985705i | \(-0.446113\pi\) | ||||
0.168483 | + | 0.985705i | \(0.446113\pi\) | |||||||
\(90\) | 2.69935 | 0.284536 | ||||||||
\(91\) | −3.78465 | −0.396739 | ||||||||
\(92\) | 11.8437 | 1.23479 | ||||||||
\(93\) | 4.13048 | 0.428311 | ||||||||
\(94\) | 12.1591 | 1.25412 | ||||||||
\(95\) | −8.40701 | −0.862541 | ||||||||
\(96\) | 6.60695 | 0.674319 | ||||||||
\(97\) | −15.6599 | −1.59002 | −0.795010 | − | 0.606597i | \(-0.792534\pi\) | ||||
−0.795010 | + | 0.606597i | \(0.792534\pi\) | |||||||
\(98\) | −2.24191 | −0.226467 | ||||||||
\(99\) | 3.48348 | 0.350103 | ||||||||
\(100\) | −10.7437 | −1.07437 | ||||||||
\(101\) | −7.53953 | −0.750211 | −0.375106 | − | 0.926982i | \(-0.622394\pi\) | ||||
−0.375106 | + | 0.926982i | \(0.622394\pi\) | |||||||
\(102\) | −8.30386 | −0.822204 | ||||||||
\(103\) | 8.05022 | 0.793212 | 0.396606 | − | 0.917989i | \(-0.370188\pi\) | ||||
0.396606 | + | 0.917989i | \(0.370188\pi\) | |||||||
\(104\) | −8.70667 | −0.853760 | ||||||||
\(105\) | 1.20404 | 0.117502 | ||||||||
\(106\) | −12.8687 | −1.24992 | ||||||||
\(107\) | 19.3415 | 1.86981 | 0.934907 | − | 0.354893i | \(-0.115483\pi\) | ||||
0.934907 | + | 0.354893i | \(0.115483\pi\) | |||||||
\(108\) | 3.02615 | 0.291191 | ||||||||
\(109\) | 14.6812 | 1.40620 | 0.703102 | − | 0.711089i | \(-0.251798\pi\) | ||||
0.703102 | + | 0.711089i | \(0.251798\pi\) | |||||||
\(110\) | 9.40311 | 0.896551 | ||||||||
\(111\) | −6.15109 | −0.583836 | ||||||||
\(112\) | 0.894732 | 0.0845443 | ||||||||
\(113\) | −19.0832 | −1.79519 | −0.897597 | − | 0.440817i | \(-0.854689\pi\) | ||||
−0.897597 | + | 0.440817i | \(0.854689\pi\) | |||||||
\(114\) | −15.6538 | −1.46611 | ||||||||
\(115\) | −4.71237 | −0.439431 | ||||||||
\(116\) | 24.3234 | 2.25838 | ||||||||
\(117\) | 3.78465 | 0.349891 | ||||||||
\(118\) | −3.01644 | −0.277686 | ||||||||
\(119\) | −3.70393 | −0.339538 | ||||||||
\(120\) | 2.76992 | 0.252858 | ||||||||
\(121\) | 1.13462 | 0.103148 | ||||||||
\(122\) | −7.01675 | −0.635267 | ||||||||
\(123\) | 11.3772 | 1.02584 | ||||||||
\(124\) | 12.4994 | 1.12248 | ||||||||
\(125\) | 10.2949 | 0.920803 | ||||||||
\(126\) | 2.24191 | 0.199725 | ||||||||
\(127\) | 3.15585 | 0.280036 | 0.140018 | − | 0.990149i | \(-0.455284\pi\) | ||||
0.140018 | + | 0.990149i | \(0.455284\pi\) | |||||||
\(128\) | 15.9818 | 1.41260 | ||||||||
\(129\) | −9.34313 | −0.822617 | ||||||||
\(130\) | 10.2161 | 0.896009 | ||||||||
\(131\) | 7.62953 | 0.666595 | 0.333298 | − | 0.942822i | \(-0.391839\pi\) | ||||
0.333298 | + | 0.942822i | \(0.391839\pi\) | |||||||
\(132\) | 10.5415 | 0.917521 | ||||||||
\(133\) | −6.98234 | −0.605446 | ||||||||
\(134\) | 11.7545 | 1.01544 | ||||||||
\(135\) | −1.20404 | −0.103627 | ||||||||
\(136\) | −8.52097 | −0.730667 | ||||||||
\(137\) | 8.15512 | 0.696739 | 0.348369 | − | 0.937357i | \(-0.386735\pi\) | ||||
0.348369 | + | 0.937357i | \(0.386735\pi\) | |||||||
\(138\) | −8.77437 | −0.746924 | ||||||||
\(139\) | −1.42536 | −0.120898 | −0.0604488 | − | 0.998171i | \(-0.519253\pi\) | ||||
−0.0604488 | + | 0.998171i | \(0.519253\pi\) | |||||||
\(140\) | 3.64360 | 0.307940 | ||||||||
\(141\) | −5.42356 | −0.456746 | ||||||||
\(142\) | 21.9118 | 1.83880 | ||||||||
\(143\) | 13.1837 | 1.10248 | ||||||||
\(144\) | −0.894732 | −0.0745610 | ||||||||
\(145\) | −9.67779 | −0.803697 | ||||||||
\(146\) | −11.9742 | −0.990992 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −18.6141 | −1.53007 | ||||||||
\(149\) | −4.93512 | −0.404301 | −0.202150 | − | 0.979354i | \(-0.564793\pi\) | ||||
−0.202150 | + | 0.979354i | \(0.564793\pi\) | |||||||
\(150\) | 7.95941 | 0.649884 | ||||||||
\(151\) | 15.3850 | 1.25202 | 0.626008 | − | 0.779816i | \(-0.284688\pi\) | ||||
0.626008 | + | 0.779816i | \(0.284688\pi\) | |||||||
\(152\) | −16.0630 | −1.30288 | ||||||||
\(153\) | 3.70393 | 0.299445 | ||||||||
\(154\) | 7.80963 | 0.629318 | ||||||||
\(155\) | −4.97327 | −0.399462 | ||||||||
\(156\) | 11.4529 | 0.916966 | ||||||||
\(157\) | 11.4028 | 0.910044 | 0.455022 | − | 0.890480i | \(-0.349631\pi\) | ||||
0.455022 | + | 0.890480i | \(0.349631\pi\) | |||||||
\(158\) | 22.1380 | 1.76120 | ||||||||
\(159\) | 5.74006 | 0.455217 | ||||||||
\(160\) | −7.95504 | −0.628901 | ||||||||
\(161\) | −3.91380 | −0.308451 | ||||||||
\(162\) | −2.24191 | −0.176141 | ||||||||
\(163\) | −16.5861 | −1.29912 | −0.649560 | − | 0.760310i | \(-0.725047\pi\) | ||||
−0.649560 | + | 0.760310i | \(0.725047\pi\) | |||||||
\(164\) | 34.4290 | 2.68845 | ||||||||
\(165\) | −4.19425 | −0.326522 | ||||||||
\(166\) | 26.1706 | 2.03123 | ||||||||
\(167\) | 14.6374 | 1.13268 | 0.566339 | − | 0.824173i | \(-0.308359\pi\) | ||||
0.566339 | + | 0.824173i | \(0.308359\pi\) | |||||||
\(168\) | 2.30052 | 0.177489 | ||||||||
\(169\) | 1.32357 | 0.101813 | ||||||||
\(170\) | 9.99818 | 0.766825 | ||||||||
\(171\) | 6.98234 | 0.533953 | ||||||||
\(172\) | −28.2737 | −2.15585 | ||||||||
\(173\) | 8.48872 | 0.645386 | 0.322693 | − | 0.946504i | \(-0.395412\pi\) | ||||
0.322693 | + | 0.946504i | \(0.395412\pi\) | |||||||
\(174\) | −18.0199 | −1.36609 | ||||||||
\(175\) | 3.55029 | 0.268377 | ||||||||
\(176\) | −3.11678 | −0.234936 | ||||||||
\(177\) | 1.34548 | 0.101132 | ||||||||
\(178\) | −7.12685 | −0.534180 | ||||||||
\(179\) | −21.9329 | −1.63934 | −0.819672 | − | 0.572833i | \(-0.805844\pi\) | ||||
−0.819672 | + | 0.572833i | \(0.805844\pi\) | |||||||
\(180\) | −3.64360 | −0.271578 | ||||||||
\(181\) | 10.8383 | 0.805601 | 0.402800 | − | 0.915288i | \(-0.368037\pi\) | ||||
0.402800 | + | 0.915288i | \(0.368037\pi\) | |||||||
\(182\) | 8.48483 | 0.628937 | ||||||||
\(183\) | 3.12982 | 0.231363 | ||||||||
\(184\) | −9.00379 | −0.663768 | ||||||||
\(185\) | 7.40616 | 0.544511 | ||||||||
\(186\) | −9.26016 | −0.678988 | ||||||||
\(187\) | 12.9025 | 0.943528 | ||||||||
\(188\) | −16.4125 | −1.19700 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 18.8477 | 1.36736 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | −13.0227 | −0.939833 | ||||||||
\(193\) | −0.363700 | −0.0261797 | −0.0130898 | − | 0.999914i | \(-0.504167\pi\) | ||||
−0.0130898 | + | 0.999914i | \(0.504167\pi\) | |||||||
\(194\) | 35.1080 | 2.52061 | ||||||||
\(195\) | −4.55687 | −0.326324 | ||||||||
\(196\) | 3.02615 | 0.216153 | ||||||||
\(197\) | −19.9462 | −1.42110 | −0.710552 | − | 0.703644i | \(-0.751555\pi\) | ||||
−0.710552 | + | 0.703644i | \(0.751555\pi\) | |||||||
\(198\) | −7.80963 | −0.555007 | ||||||||
\(199\) | 11.1531 | 0.790625 | 0.395313 | − | 0.918547i | \(-0.370636\pi\) | ||||
0.395313 | + | 0.918547i | \(0.370636\pi\) | |||||||
\(200\) | 8.16752 | 0.577531 | ||||||||
\(201\) | −5.24309 | −0.369819 | ||||||||
\(202\) | 16.9029 | 1.18929 | ||||||||
\(203\) | −8.03776 | −0.564140 | ||||||||
\(204\) | 11.2086 | 0.784761 | ||||||||
\(205\) | −13.6986 | −0.956749 | ||||||||
\(206\) | −18.0478 | −1.25745 | ||||||||
\(207\) | 3.91380 | 0.272028 | ||||||||
\(208\) | −3.38625 | −0.234794 | ||||||||
\(209\) | 24.3228 | 1.68245 | ||||||||
\(210\) | −2.69935 | −0.186273 | ||||||||
\(211\) | −4.33910 | −0.298716 | −0.149358 | − | 0.988783i | \(-0.547721\pi\) | ||||
−0.149358 | + | 0.988783i | \(0.547721\pi\) | |||||||
\(212\) | 17.3703 | 1.19299 | ||||||||
\(213\) | −9.77372 | −0.669684 | ||||||||
\(214\) | −43.3618 | −2.96415 | ||||||||
\(215\) | 11.2495 | 0.767210 | ||||||||
\(216\) | −2.30052 | −0.156531 | ||||||||
\(217\) | −4.13048 | −0.280395 | ||||||||
\(218\) | −32.9139 | −2.22921 | ||||||||
\(219\) | 5.34108 | 0.360917 | ||||||||
\(220\) | −12.6924 | −0.855722 | ||||||||
\(221\) | 14.0181 | 0.942957 | ||||||||
\(222\) | 13.7902 | 0.925536 | ||||||||
\(223\) | −4.94454 | −0.331111 | −0.165556 | − | 0.986200i | \(-0.552942\pi\) | ||||
−0.165556 | + | 0.986200i | \(0.552942\pi\) | |||||||
\(224\) | −6.60695 | −0.441446 | ||||||||
\(225\) | −3.55029 | −0.236686 | ||||||||
\(226\) | 42.7827 | 2.84586 | ||||||||
\(227\) | 27.0946 | 1.79833 | 0.899165 | − | 0.437610i | \(-0.144175\pi\) | ||||
0.899165 | + | 0.437610i | \(0.144175\pi\) | |||||||
\(228\) | 21.1296 | 1.39934 | ||||||||
\(229\) | −14.5531 | −0.961695 | −0.480848 | − | 0.876804i | \(-0.659671\pi\) | ||||
−0.480848 | + | 0.876804i | \(0.659671\pi\) | |||||||
\(230\) | 10.5647 | 0.696615 | ||||||||
\(231\) | −3.48348 | −0.229196 | ||||||||
\(232\) | −18.4911 | −1.21400 | ||||||||
\(233\) | 8.11619 | 0.531709 | 0.265855 | − | 0.964013i | \(-0.414346\pi\) | ||||
0.265855 | + | 0.964013i | \(0.414346\pi\) | |||||||
\(234\) | −8.48483 | −0.554671 | ||||||||
\(235\) | 6.53019 | 0.425982 | ||||||||
\(236\) | 4.07162 | 0.265040 | ||||||||
\(237\) | −9.87463 | −0.641426 | ||||||||
\(238\) | 8.30386 | 0.538259 | ||||||||
\(239\) | −1.89186 | −0.122374 | −0.0611870 | − | 0.998126i | \(-0.519489\pi\) | ||||
−0.0611870 | + | 0.998126i | \(0.519489\pi\) | |||||||
\(240\) | 1.07729 | 0.0695390 | ||||||||
\(241\) | −8.61286 | −0.554803 | −0.277402 | − | 0.960754i | \(-0.589473\pi\) | ||||
−0.277402 | + | 0.960754i | \(0.589473\pi\) | |||||||
\(242\) | −2.54372 | −0.163517 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 9.47128 | 0.606336 | ||||||||
\(245\) | −1.20404 | −0.0769233 | ||||||||
\(246\) | −25.5065 | −1.62624 | ||||||||
\(247\) | 26.4257 | 1.68143 | ||||||||
\(248\) | −9.50228 | −0.603395 | ||||||||
\(249\) | −11.6734 | −0.739770 | ||||||||
\(250\) | −23.0802 | −1.45972 | ||||||||
\(251\) | −15.7496 | −0.994107 | −0.497054 | − | 0.867720i | \(-0.665585\pi\) | ||||
−0.497054 | + | 0.867720i | \(0.665585\pi\) | |||||||
\(252\) | −3.02615 | −0.190629 | ||||||||
\(253\) | 13.6336 | 0.857139 | ||||||||
\(254\) | −7.07512 | −0.443932 | ||||||||
\(255\) | −4.45968 | −0.279276 | ||||||||
\(256\) | −9.78427 | −0.611517 | ||||||||
\(257\) | 24.8268 | 1.54865 | 0.774327 | − | 0.632786i | \(-0.218089\pi\) | ||||
0.774327 | + | 0.632786i | \(0.218089\pi\) | |||||||
\(258\) | 20.9464 | 1.30407 | ||||||||
\(259\) | 6.15109 | 0.382210 | ||||||||
\(260\) | −13.7897 | −0.855204 | ||||||||
\(261\) | 8.03776 | 0.497525 | ||||||||
\(262\) | −17.1047 | −1.05673 | ||||||||
\(263\) | 26.0980 | 1.60927 | 0.804637 | − | 0.593767i | \(-0.202360\pi\) | ||||
0.804637 | + | 0.593767i | \(0.202360\pi\) | |||||||
\(264\) | −8.01383 | −0.493217 | ||||||||
\(265\) | −6.91126 | −0.424556 | ||||||||
\(266\) | 15.6538 | 0.959793 | ||||||||
\(267\) | 3.17892 | 0.194547 | ||||||||
\(268\) | −15.8664 | −0.969193 | ||||||||
\(269\) | −21.2558 | −1.29599 | −0.647995 | − | 0.761644i | \(-0.724392\pi\) | ||||
−0.647995 | + | 0.761644i | \(0.724392\pi\) | |||||||
\(270\) | 2.69935 | 0.164277 | ||||||||
\(271\) | −14.8459 | −0.901821 | −0.450911 | − | 0.892569i | \(-0.648901\pi\) | ||||
−0.450911 | + | 0.892569i | \(0.648901\pi\) | |||||||
\(272\) | −3.31402 | −0.200942 | ||||||||
\(273\) | −3.78465 | −0.229057 | ||||||||
\(274\) | −18.2830 | −1.10452 | ||||||||
\(275\) | −12.3674 | −0.745779 | ||||||||
\(276\) | 11.8437 | 0.712909 | ||||||||
\(277\) | −17.8482 | −1.07240 | −0.536198 | − | 0.844092i | \(-0.680140\pi\) | ||||
−0.536198 | + | 0.844092i | \(0.680140\pi\) | |||||||
\(278\) | 3.19553 | 0.191655 | ||||||||
\(279\) | 4.13048 | 0.247286 | ||||||||
\(280\) | −2.76992 | −0.165535 | ||||||||
\(281\) | −2.89496 | −0.172699 | −0.0863494 | − | 0.996265i | \(-0.527520\pi\) | ||||
−0.0863494 | + | 0.996265i | \(0.527520\pi\) | |||||||
\(282\) | 12.1591 | 0.724065 | ||||||||
\(283\) | −25.7601 | −1.53128 | −0.765640 | − | 0.643269i | \(-0.777578\pi\) | ||||
−0.765640 | + | 0.643269i | \(0.777578\pi\) | |||||||
\(284\) | −29.5767 | −1.75505 | ||||||||
\(285\) | −8.40701 | −0.497988 | ||||||||
\(286\) | −29.5567 | −1.74773 | ||||||||
\(287\) | −11.3772 | −0.671573 | ||||||||
\(288\) | 6.60695 | 0.389318 | ||||||||
\(289\) | −3.28093 | −0.192996 | ||||||||
\(290\) | 21.6967 | 1.27407 | ||||||||
\(291\) | −15.6599 | −0.917998 | ||||||||
\(292\) | 16.1629 | 0.945861 | ||||||||
\(293\) | −26.5108 | −1.54878 | −0.774390 | − | 0.632709i | \(-0.781943\pi\) | ||||
−0.774390 | + | 0.632709i | \(0.781943\pi\) | |||||||
\(294\) | −2.24191 | −0.130751 | ||||||||
\(295\) | −1.62001 | −0.0943207 | ||||||||
\(296\) | 14.1507 | 0.822494 | ||||||||
\(297\) | 3.48348 | 0.202132 | ||||||||
\(298\) | 11.0641 | 0.640925 | ||||||||
\(299\) | 14.8124 | 0.856621 | ||||||||
\(300\) | −10.7437 | −0.620287 | ||||||||
\(301\) | 9.34313 | 0.538529 | ||||||||
\(302\) | −34.4918 | −1.98478 | ||||||||
\(303\) | −7.53953 | −0.433135 | ||||||||
\(304\) | −6.24732 | −0.358309 | ||||||||
\(305\) | −3.76842 | −0.215779 | ||||||||
\(306\) | −8.30386 | −0.474700 | ||||||||
\(307\) | 8.26367 | 0.471632 | 0.235816 | − | 0.971798i | \(-0.424224\pi\) | ||||
0.235816 | + | 0.971798i | \(0.424224\pi\) | |||||||
\(308\) | −10.5415 | −0.600659 | ||||||||
\(309\) | 8.05022 | 0.457961 | ||||||||
\(310\) | 11.1496 | 0.633255 | ||||||||
\(311\) | 0.313790 | 0.0177934 | 0.00889671 | − | 0.999960i | \(-0.497168\pi\) | ||||
0.00889671 | + | 0.999960i | \(0.497168\pi\) | |||||||
\(312\) | −8.70667 | −0.492918 | ||||||||
\(313\) | −30.6173 | −1.73059 | −0.865297 | − | 0.501259i | \(-0.832870\pi\) | ||||
−0.865297 | + | 0.501259i | \(0.832870\pi\) | |||||||
\(314\) | −25.5640 | −1.44266 | ||||||||
\(315\) | 1.20404 | 0.0678400 | ||||||||
\(316\) | −29.8821 | −1.68100 | ||||||||
\(317\) | 19.4228 | 1.09089 | 0.545447 | − | 0.838145i | \(-0.316360\pi\) | ||||
0.545447 | + | 0.838145i | \(0.316360\pi\) | |||||||
\(318\) | −12.8687 | −0.721640 | ||||||||
\(319\) | 27.9994 | 1.56766 | ||||||||
\(320\) | 15.6799 | 0.876531 | ||||||||
\(321\) | 19.3415 | 1.07954 | ||||||||
\(322\) | 8.77437 | 0.488977 | ||||||||
\(323\) | 25.8621 | 1.43900 | ||||||||
\(324\) | 3.02615 | 0.168119 | ||||||||
\(325\) | −13.4366 | −0.745328 | ||||||||
\(326\) | 37.1844 | 2.05945 | ||||||||
\(327\) | 14.6812 | 0.811872 | ||||||||
\(328\) | −26.1734 | −1.44519 | ||||||||
\(329\) | 5.42356 | 0.299011 | ||||||||
\(330\) | 9.40311 | 0.517624 | ||||||||
\(331\) | −7.14609 | −0.392785 | −0.196392 | − | 0.980525i | \(-0.562923\pi\) | ||||
−0.196392 | + | 0.980525i | \(0.562923\pi\) | |||||||
\(332\) | −35.3253 | −1.93873 | ||||||||
\(333\) | −6.15109 | −0.337078 | ||||||||
\(334\) | −32.8157 | −1.79560 | ||||||||
\(335\) | 6.31289 | 0.344910 | ||||||||
\(336\) | 0.894732 | 0.0488117 | ||||||||
\(337\) | −9.81641 | −0.534734 | −0.267367 | − | 0.963595i | \(-0.586154\pi\) | ||||
−0.267367 | + | 0.963595i | \(0.586154\pi\) | |||||||
\(338\) | −2.96732 | −0.161401 | ||||||||
\(339\) | −19.0832 | −1.03646 | ||||||||
\(340\) | −13.4956 | −0.731903 | ||||||||
\(341\) | 14.3885 | 0.779178 | ||||||||
\(342\) | −15.6538 | −0.846458 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 21.4941 | 1.15888 | ||||||||
\(345\) | −4.71237 | −0.253706 | ||||||||
\(346\) | −19.0309 | −1.02311 | ||||||||
\(347\) | 22.4398 | 1.20463 | 0.602317 | − | 0.798257i | \(-0.294244\pi\) | ||||
0.602317 | + | 0.798257i | \(0.294244\pi\) | |||||||
\(348\) | 24.3234 | 1.30387 | ||||||||
\(349\) | 18.1408 | 0.971052 | 0.485526 | − | 0.874222i | \(-0.338628\pi\) | ||||
0.485526 | + | 0.874222i | \(0.338628\pi\) | |||||||
\(350\) | −7.95941 | −0.425449 | ||||||||
\(351\) | 3.78465 | 0.202010 | ||||||||
\(352\) | 23.0152 | 1.22671 | ||||||||
\(353\) | −8.72050 | −0.464145 | −0.232073 | − | 0.972698i | \(-0.574551\pi\) | ||||
−0.232073 | + | 0.972698i | \(0.574551\pi\) | |||||||
\(354\) | −3.01644 | −0.160322 | ||||||||
\(355\) | 11.7680 | 0.624578 | ||||||||
\(356\) | 9.61989 | 0.509853 | ||||||||
\(357\) | −3.70393 | −0.196033 | ||||||||
\(358\) | 49.1716 | 2.59880 | ||||||||
\(359\) | 33.8229 | 1.78510 | 0.892552 | − | 0.450944i | \(-0.148913\pi\) | ||||
0.892552 | + | 0.450944i | \(0.148913\pi\) | |||||||
\(360\) | 2.76992 | 0.145988 | ||||||||
\(361\) | 29.7530 | 1.56595 | ||||||||
\(362\) | −24.2984 | −1.27709 | ||||||||
\(363\) | 1.13462 | 0.0595523 | ||||||||
\(364\) | −11.4529 | −0.600295 | ||||||||
\(365\) | −6.43087 | −0.336607 | ||||||||
\(366\) | −7.01675 | −0.366772 | ||||||||
\(367\) | 2.21897 | 0.115829 | 0.0579145 | − | 0.998322i | \(-0.481555\pi\) | ||||
0.0579145 | + | 0.998322i | \(0.481555\pi\) | |||||||
\(368\) | −3.50180 | −0.182544 | ||||||||
\(369\) | 11.3772 | 0.592272 | ||||||||
\(370\) | −16.6039 | −0.863196 | ||||||||
\(371\) | −5.74006 | −0.298009 | ||||||||
\(372\) | 12.4994 | 0.648066 | ||||||||
\(373\) | 14.9552 | 0.774353 | 0.387176 | − | 0.922006i | \(-0.373450\pi\) | ||||
0.387176 | + | 0.922006i | \(0.373450\pi\) | |||||||
\(374\) | −28.9263 | −1.49574 | ||||||||
\(375\) | 10.2949 | 0.531626 | ||||||||
\(376\) | 12.4770 | 0.643454 | ||||||||
\(377\) | 30.4201 | 1.56672 | ||||||||
\(378\) | 2.24191 | 0.115311 | ||||||||
\(379\) | −17.2744 | −0.887326 | −0.443663 | − | 0.896194i | \(-0.646321\pi\) | ||||
−0.443663 | + | 0.896194i | \(0.646321\pi\) | |||||||
\(380\) | −25.4408 | −1.30509 | ||||||||
\(381\) | 3.15585 | 0.161679 | ||||||||
\(382\) | 2.24191 | 0.114706 | ||||||||
\(383\) | −16.5466 | −0.845491 | −0.422746 | − | 0.906248i | \(-0.638934\pi\) | ||||
−0.422746 | + | 0.906248i | \(0.638934\pi\) | |||||||
\(384\) | 15.9818 | 0.815568 | ||||||||
\(385\) | 4.19425 | 0.213759 | ||||||||
\(386\) | 0.815381 | 0.0415018 | ||||||||
\(387\) | −9.34313 | −0.474938 | ||||||||
\(388\) | −47.3891 | −2.40582 | ||||||||
\(389\) | 27.7619 | 1.40758 | 0.703792 | − | 0.710406i | \(-0.251489\pi\) | ||||
0.703792 | + | 0.710406i | \(0.251489\pi\) | |||||||
\(390\) | 10.2161 | 0.517311 | ||||||||
\(391\) | 14.4964 | 0.733116 | ||||||||
\(392\) | −2.30052 | −0.116194 | ||||||||
\(393\) | 7.62953 | 0.384859 | ||||||||
\(394\) | 44.7174 | 2.25283 | ||||||||
\(395\) | 11.8894 | 0.598223 | ||||||||
\(396\) | 10.5415 | 0.529731 | ||||||||
\(397\) | 9.44996 | 0.474280 | 0.237140 | − | 0.971476i | \(-0.423790\pi\) | ||||
0.237140 | + | 0.971476i | \(0.423790\pi\) | |||||||
\(398\) | −25.0043 | −1.25335 | ||||||||
\(399\) | −6.98234 | −0.349554 | ||||||||
\(400\) | 3.17656 | 0.158828 | ||||||||
\(401\) | −9.59080 | −0.478942 | −0.239471 | − | 0.970904i | \(-0.576974\pi\) | ||||
−0.239471 | + | 0.970904i | \(0.576974\pi\) | |||||||
\(402\) | 11.7545 | 0.586263 | ||||||||
\(403\) | 15.6324 | 0.778707 | ||||||||
\(404\) | −22.8157 | −1.13512 | ||||||||
\(405\) | −1.20404 | −0.0598292 | ||||||||
\(406\) | 18.0199 | 0.894313 | ||||||||
\(407\) | −21.4272 | −1.06211 | ||||||||
\(408\) | −8.52097 | −0.421851 | ||||||||
\(409\) | −6.71584 | −0.332077 | −0.166038 | − | 0.986119i | \(-0.553098\pi\) | ||||
−0.166038 | + | 0.986119i | \(0.553098\pi\) | |||||||
\(410\) | 30.7109 | 1.51670 | ||||||||
\(411\) | 8.15512 | 0.402262 | ||||||||
\(412\) | 24.3612 | 1.20019 | ||||||||
\(413\) | −1.34548 | −0.0662067 | ||||||||
\(414\) | −8.77437 | −0.431237 | ||||||||
\(415\) | 14.0552 | 0.689943 | ||||||||
\(416\) | 25.0050 | 1.22597 | ||||||||
\(417\) | −1.42536 | −0.0698002 | ||||||||
\(418\) | −54.5295 | −2.66713 | ||||||||
\(419\) | 27.7068 | 1.35357 | 0.676783 | − | 0.736183i | \(-0.263374\pi\) | ||||
0.676783 | + | 0.736183i | \(0.263374\pi\) | |||||||
\(420\) | 3.64360 | 0.177789 | ||||||||
\(421\) | 25.0634 | 1.22152 | 0.610758 | − | 0.791817i | \(-0.290865\pi\) | ||||
0.610758 | + | 0.791817i | \(0.290865\pi\) | |||||||
\(422\) | 9.72785 | 0.473544 | ||||||||
\(423\) | −5.42356 | −0.263703 | ||||||||
\(424\) | −13.2051 | −0.641299 | ||||||||
\(425\) | −13.1500 | −0.637869 | ||||||||
\(426\) | 21.9118 | 1.06163 | ||||||||
\(427\) | −3.12982 | −0.151462 | ||||||||
\(428\) | 58.5302 | 2.82916 | ||||||||
\(429\) | 13.1837 | 0.636517 | ||||||||
\(430\) | −25.2203 | −1.21623 | ||||||||
\(431\) | −5.64021 | −0.271679 | −0.135840 | − | 0.990731i | \(-0.543373\pi\) | ||||
−0.135840 | + | 0.990731i | \(0.543373\pi\) | |||||||
\(432\) | −0.894732 | −0.0430478 | ||||||||
\(433\) | 29.4570 | 1.41561 | 0.707807 | − | 0.706406i | \(-0.249685\pi\) | ||||
0.707807 | + | 0.706406i | \(0.249685\pi\) | |||||||
\(434\) | 9.26016 | 0.444502 | ||||||||
\(435\) | −9.67779 | −0.464014 | ||||||||
\(436\) | 44.4275 | 2.12769 | ||||||||
\(437\) | 27.3275 | 1.30725 | ||||||||
\(438\) | −11.9742 | −0.572149 | ||||||||
\(439\) | 24.3111 | 1.16030 | 0.580152 | − | 0.814508i | \(-0.302993\pi\) | ||||
0.580152 | + | 0.814508i | \(0.302993\pi\) | |||||||
\(440\) | 9.64897 | 0.459996 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −31.4272 | −1.49484 | ||||||||
\(443\) | 15.0832 | 0.716624 | 0.358312 | − | 0.933602i | \(-0.383352\pi\) | ||||
0.358312 | + | 0.933602i | \(0.383352\pi\) | |||||||
\(444\) | −18.6141 | −0.883386 | ||||||||
\(445\) | −3.82755 | −0.181443 | ||||||||
\(446\) | 11.0852 | 0.524900 | ||||||||
\(447\) | −4.93512 | −0.233423 | ||||||||
\(448\) | 13.0227 | 0.615265 | ||||||||
\(449\) | 32.6603 | 1.54133 | 0.770667 | − | 0.637239i | \(-0.219923\pi\) | ||||
0.770667 | + | 0.637239i | \(0.219923\pi\) | |||||||
\(450\) | 7.95941 | 0.375210 | ||||||||
\(451\) | 39.6321 | 1.86620 | ||||||||
\(452\) | −57.7485 | −2.71626 | ||||||||
\(453\) | 15.3850 | 0.722852 | ||||||||
\(454\) | −60.7435 | −2.85083 | ||||||||
\(455\) | 4.55687 | 0.213629 | ||||||||
\(456\) | −16.0630 | −0.752221 | ||||||||
\(457\) | 6.68108 | 0.312528 | 0.156264 | − | 0.987715i | \(-0.450055\pi\) | ||||
0.156264 | + | 0.987715i | \(0.450055\pi\) | |||||||
\(458\) | 32.6267 | 1.52454 | ||||||||
\(459\) | 3.70393 | 0.172884 | ||||||||
\(460\) | −14.2603 | −0.664891 | ||||||||
\(461\) | 37.4914 | 1.74615 | 0.873073 | − | 0.487589i | \(-0.162123\pi\) | ||||
0.873073 | + | 0.487589i | \(0.162123\pi\) | |||||||
\(462\) | 7.80963 | 0.363337 | ||||||||
\(463\) | −31.2404 | −1.45186 | −0.725931 | − | 0.687767i | \(-0.758591\pi\) | ||||
−0.725931 | + | 0.687767i | \(0.758591\pi\) | |||||||
\(464\) | −7.19165 | −0.333864 | ||||||||
\(465\) | −4.97327 | −0.230630 | ||||||||
\(466\) | −18.1957 | −0.842902 | ||||||||
\(467\) | −23.2059 | −1.07384 | −0.536922 | − | 0.843632i | \(-0.680413\pi\) | ||||
−0.536922 | + | 0.843632i | \(0.680413\pi\) | |||||||
\(468\) | 11.4529 | 0.529411 | ||||||||
\(469\) | 5.24309 | 0.242104 | ||||||||
\(470\) | −14.6401 | −0.675296 | ||||||||
\(471\) | 11.4028 | 0.525414 | ||||||||
\(472\) | −3.09531 | −0.142473 | ||||||||
\(473\) | −32.5466 | −1.49649 | ||||||||
\(474\) | 22.1380 | 1.01683 | ||||||||
\(475\) | −24.7893 | −1.13741 | ||||||||
\(476\) | −11.2086 | −0.513746 | ||||||||
\(477\) | 5.74006 | 0.262819 | ||||||||
\(478\) | 4.24136 | 0.193995 | ||||||||
\(479\) | −11.7326 | −0.536074 | −0.268037 | − | 0.963409i | \(-0.586375\pi\) | ||||
−0.268037 | + | 0.963409i | \(0.586375\pi\) | |||||||
\(480\) | −7.95504 | −0.363096 | ||||||||
\(481\) | −23.2797 | −1.06146 | ||||||||
\(482\) | 19.3092 | 0.879511 | ||||||||
\(483\) | −3.91380 | −0.178084 | ||||||||
\(484\) | 3.43354 | 0.156070 | ||||||||
\(485\) | 18.8551 | 0.856167 | ||||||||
\(486\) | −2.24191 | −0.101695 | ||||||||
\(487\) | 40.5988 | 1.83971 | 0.919854 | − | 0.392262i | \(-0.128307\pi\) | ||||
0.919854 | + | 0.392262i | \(0.128307\pi\) | |||||||
\(488\) | −7.20021 | −0.325938 | ||||||||
\(489\) | −16.5861 | −0.750047 | ||||||||
\(490\) | 2.69935 | 0.121944 | ||||||||
\(491\) | −39.8124 | −1.79671 | −0.898355 | − | 0.439270i | \(-0.855237\pi\) | ||||
−0.898355 | + | 0.439270i | \(0.855237\pi\) | |||||||
\(492\) | 34.4290 | 1.55218 | ||||||||
\(493\) | 29.7713 | 1.34083 | ||||||||
\(494\) | −59.2440 | −2.66551 | ||||||||
\(495\) | −4.19425 | −0.188517 | ||||||||
\(496\) | −3.69568 | −0.165941 | ||||||||
\(497\) | 9.77372 | 0.438411 | ||||||||
\(498\) | 26.1706 | 1.17273 | ||||||||
\(499\) | 8.09389 | 0.362332 | 0.181166 | − | 0.983453i | \(-0.442013\pi\) | ||||
0.181166 | + | 0.983453i | \(0.442013\pi\) | |||||||
\(500\) | 31.1538 | 1.39324 | ||||||||
\(501\) | 14.6374 | 0.653952 | ||||||||
\(502\) | 35.3092 | 1.57593 | ||||||||
\(503\) | −35.6865 | −1.59118 | −0.795591 | − | 0.605835i | \(-0.792839\pi\) | ||||
−0.795591 | + | 0.605835i | \(0.792839\pi\) | |||||||
\(504\) | 2.30052 | 0.102473 | ||||||||
\(505\) | 9.07790 | 0.403961 | ||||||||
\(506\) | −30.5653 | −1.35880 | ||||||||
\(507\) | 1.32357 | 0.0587817 | ||||||||
\(508\) | 9.55006 | 0.423715 | ||||||||
\(509\) | 0.0532497 | 0.00236025 | 0.00118012 | − | 0.999999i | \(-0.499624\pi\) | ||||
0.00118012 | + | 0.999999i | \(0.499624\pi\) | |||||||
\(510\) | 9.99818 | 0.442727 | ||||||||
\(511\) | −5.34108 | −0.236275 | ||||||||
\(512\) | −10.0282 | −0.443186 | ||||||||
\(513\) | 6.98234 | 0.308278 | ||||||||
\(514\) | −55.6594 | −2.45503 | ||||||||
\(515\) | −9.69279 | −0.427115 | ||||||||
\(516\) | −28.2737 | −1.24468 | ||||||||
\(517\) | −18.8929 | −0.830907 | ||||||||
\(518\) | −13.7902 | −0.605905 | ||||||||
\(519\) | 8.48872 | 0.372614 | ||||||||
\(520\) | 10.4832 | 0.459718 | ||||||||
\(521\) | −15.9384 | −0.698275 | −0.349138 | − | 0.937071i | \(-0.613525\pi\) | ||||
−0.349138 | + | 0.937071i | \(0.613525\pi\) | |||||||
\(522\) | −18.0199 | −0.788710 | ||||||||
\(523\) | 0.822676 | 0.0359731 | 0.0179866 | − | 0.999838i | \(-0.494274\pi\) | ||||
0.0179866 | + | 0.999838i | \(0.494274\pi\) | |||||||
\(524\) | 23.0881 | 1.00861 | ||||||||
\(525\) | 3.55029 | 0.154947 | ||||||||
\(526\) | −58.5094 | −2.55113 | ||||||||
\(527\) | 15.2990 | 0.666435 | ||||||||
\(528\) | −3.11678 | −0.135640 | ||||||||
\(529\) | −7.68217 | −0.334008 | ||||||||
\(530\) | 15.4944 | 0.673034 | ||||||||
\(531\) | 1.34548 | 0.0583888 | ||||||||
\(532\) | −21.1296 | −0.916083 | ||||||||
\(533\) | 43.0586 | 1.86507 | ||||||||
\(534\) | −7.12685 | −0.308409 | ||||||||
\(535\) | −23.2879 | −1.00683 | ||||||||
\(536\) | 12.0619 | 0.520993 | ||||||||
\(537\) | −21.9329 | −0.946476 | ||||||||
\(538\) | 47.6536 | 2.05449 | ||||||||
\(539\) | 3.48348 | 0.150044 | ||||||||
\(540\) | −3.64360 | −0.156796 | ||||||||
\(541\) | 32.9885 | 1.41829 | 0.709144 | − | 0.705064i | \(-0.249082\pi\) | ||||
0.709144 | + | 0.705064i | \(0.249082\pi\) | |||||||
\(542\) | 33.2830 | 1.42963 | ||||||||
\(543\) | 10.8383 | 0.465114 | ||||||||
\(544\) | 24.4717 | 1.04921 | ||||||||
\(545\) | −17.6767 | −0.757189 | ||||||||
\(546\) | 8.48483 | 0.363117 | ||||||||
\(547\) | −23.9188 | −1.02269 | −0.511347 | − | 0.859374i | \(-0.670853\pi\) | ||||
−0.511347 | + | 0.859374i | \(0.670853\pi\) | |||||||
\(548\) | 24.6786 | 1.05422 | ||||||||
\(549\) | 3.12982 | 0.133577 | ||||||||
\(550\) | 27.7265 | 1.18226 | ||||||||
\(551\) | 56.1224 | 2.39089 | ||||||||
\(552\) | −9.00379 | −0.383227 | ||||||||
\(553\) | 9.87463 | 0.419912 | ||||||||
\(554\) | 40.0141 | 1.70003 | ||||||||
\(555\) | 7.40616 | 0.314374 | ||||||||
\(556\) | −4.31335 | −0.182927 | ||||||||
\(557\) | 15.3900 | 0.652096 | 0.326048 | − | 0.945353i | \(-0.394283\pi\) | ||||
0.326048 | + | 0.945353i | \(0.394283\pi\) | |||||||
\(558\) | −9.26016 | −0.392014 | ||||||||
\(559\) | −35.3605 | −1.49559 | ||||||||
\(560\) | −1.07729 | −0.0455240 | ||||||||
\(561\) | 12.9025 | 0.544746 | ||||||||
\(562\) | 6.49023 | 0.273774 | ||||||||
\(563\) | −1.58400 | −0.0667576 | −0.0333788 | − | 0.999443i | \(-0.510627\pi\) | ||||
−0.0333788 | + | 0.999443i | \(0.510627\pi\) | |||||||
\(564\) | −16.4125 | −0.691091 | ||||||||
\(565\) | 22.9769 | 0.966645 | ||||||||
\(566\) | 57.7518 | 2.42749 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 22.4847 | 0.943436 | ||||||||
\(569\) | −7.73642 | −0.324328 | −0.162164 | − | 0.986764i | \(-0.551847\pi\) | ||||
−0.162164 | + | 0.986764i | \(0.551847\pi\) | |||||||
\(570\) | 18.8477 | 0.789445 | ||||||||
\(571\) | 15.8675 | 0.664032 | 0.332016 | − | 0.943274i | \(-0.392271\pi\) | ||||
0.332016 | + | 0.943274i | \(0.392271\pi\) | |||||||
\(572\) | 39.8959 | 1.66813 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | 25.5065 | 1.06462 | ||||||||
\(575\) | −13.8951 | −0.579466 | ||||||||
\(576\) | −13.0227 | −0.542613 | ||||||||
\(577\) | −5.37823 | −0.223899 | −0.111949 | − | 0.993714i | \(-0.535709\pi\) | ||||
−0.111949 | + | 0.993714i | \(0.535709\pi\) | |||||||
\(578\) | 7.35553 | 0.305950 | ||||||||
\(579\) | −0.363700 | −0.0151148 | ||||||||
\(580\) | −29.2864 | −1.21605 | ||||||||
\(581\) | 11.6734 | 0.484293 | ||||||||
\(582\) | 35.1080 | 1.45527 | ||||||||
\(583\) | 19.9954 | 0.828124 | ||||||||
\(584\) | −12.2873 | −0.508451 | ||||||||
\(585\) | −4.55687 | −0.188403 | ||||||||
\(586\) | 59.4348 | 2.45523 | ||||||||
\(587\) | −41.5419 | −1.71462 | −0.857308 | − | 0.514804i | \(-0.827865\pi\) | ||||
−0.857308 | + | 0.514804i | \(0.827865\pi\) | |||||||
\(588\) | 3.02615 | 0.124796 | ||||||||
\(589\) | 28.8404 | 1.18835 | ||||||||
\(590\) | 3.63191 | 0.149524 | ||||||||
\(591\) | −19.9462 | −0.820475 | ||||||||
\(592\) | 5.50358 | 0.226196 | ||||||||
\(593\) | −28.9965 | −1.19074 | −0.595372 | − | 0.803450i | \(-0.702995\pi\) | ||||
−0.595372 | + | 0.803450i | \(0.702995\pi\) | |||||||
\(594\) | −7.80963 | −0.320433 | ||||||||
\(595\) | 4.45968 | 0.182829 | ||||||||
\(596\) | −14.9344 | −0.611737 | ||||||||
\(597\) | 11.1531 | 0.456468 | ||||||||
\(598\) | −33.2079 | −1.35797 | ||||||||
\(599\) | 16.2897 | 0.665581 | 0.332790 | − | 0.943001i | \(-0.392010\pi\) | ||||
0.332790 | + | 0.943001i | \(0.392010\pi\) | |||||||
\(600\) | 8.16752 | 0.333438 | ||||||||
\(601\) | −0.713070 | −0.0290867 | −0.0145434 | − | 0.999894i | \(-0.504629\pi\) | ||||
−0.0145434 | + | 0.999894i | \(0.504629\pi\) | |||||||
\(602\) | −20.9464 | −0.853713 | ||||||||
\(603\) | −5.24309 | −0.213515 | ||||||||
\(604\) | 46.5574 | 1.89439 | ||||||||
\(605\) | −1.36613 | −0.0555412 | ||||||||
\(606\) | 16.9029 | 0.686634 | ||||||||
\(607\) | 28.0452 | 1.13832 | 0.569160 | − | 0.822227i | \(-0.307269\pi\) | ||||
0.569160 | + | 0.822227i | \(0.307269\pi\) | |||||||
\(608\) | 46.1320 | 1.87090 | ||||||||
\(609\) | −8.03776 | −0.325707 | ||||||||
\(610\) | 8.44845 | 0.342068 | ||||||||
\(611\) | −20.5263 | −0.830405 | ||||||||
\(612\) | 11.2086 | 0.453082 | ||||||||
\(613\) | −10.4533 | −0.422204 | −0.211102 | − | 0.977464i | \(-0.567705\pi\) | ||||
−0.211102 | + | 0.977464i | \(0.567705\pi\) | |||||||
\(614\) | −18.5264 | −0.747663 | ||||||||
\(615\) | −13.6986 | −0.552379 | ||||||||
\(616\) | 8.01383 | 0.322886 | ||||||||
\(617\) | −12.9503 | −0.521360 | −0.260680 | − | 0.965425i | \(-0.583947\pi\) | ||||
−0.260680 | + | 0.965425i | \(0.583947\pi\) | |||||||
\(618\) | −18.0478 | −0.725991 | ||||||||
\(619\) | 10.0372 | 0.403428 | 0.201714 | − | 0.979444i | \(-0.435349\pi\) | ||||
0.201714 | + | 0.979444i | \(0.435349\pi\) | |||||||
\(620\) | −15.0498 | −0.604416 | ||||||||
\(621\) | 3.91380 | 0.157055 | ||||||||
\(622\) | −0.703489 | −0.0282073 | ||||||||
\(623\) | −3.17892 | −0.127361 | ||||||||
\(624\) | −3.38625 | −0.135558 | ||||||||
\(625\) | 5.35599 | 0.214239 | ||||||||
\(626\) | 68.6412 | 2.74346 | ||||||||
\(627\) | 24.3228 | 0.971360 | ||||||||
\(628\) | 34.5066 | 1.37696 | ||||||||
\(629\) | −22.7832 | −0.908425 | ||||||||
\(630\) | −2.69935 | −0.107544 | ||||||||
\(631\) | 31.1599 | 1.24045 | 0.620227 | − | 0.784422i | \(-0.287040\pi\) | ||||
0.620227 | + | 0.784422i | \(0.287040\pi\) | |||||||
\(632\) | 22.7168 | 0.903626 | ||||||||
\(633\) | −4.33910 | −0.172464 | ||||||||
\(634\) | −43.5442 | −1.72936 | ||||||||
\(635\) | −3.79977 | −0.150789 | ||||||||
\(636\) | 17.3703 | 0.688776 | ||||||||
\(637\) | 3.78465 | 0.149953 | ||||||||
\(638\) | −62.7720 | −2.48517 | ||||||||
\(639\) | −9.77372 | −0.386642 | ||||||||
\(640\) | −19.2427 | −0.760635 | ||||||||
\(641\) | 28.9842 | 1.14481 | 0.572403 | − | 0.819973i | \(-0.306011\pi\) | ||||
0.572403 | + | 0.819973i | \(0.306011\pi\) | |||||||
\(642\) | −43.3618 | −1.71136 | ||||||||
\(643\) | 5.24635 | 0.206896 | 0.103448 | − | 0.994635i | \(-0.467012\pi\) | ||||
0.103448 | + | 0.994635i | \(0.467012\pi\) | |||||||
\(644\) | −11.8437 | −0.466708 | ||||||||
\(645\) | 11.2495 | 0.442949 | ||||||||
\(646\) | −57.9803 | −2.28121 | ||||||||
\(647\) | −38.5783 | −1.51667 | −0.758334 | − | 0.651866i | \(-0.773986\pi\) | ||||
−0.758334 | + | 0.651866i | \(0.773986\pi\) | |||||||
\(648\) | −2.30052 | −0.0903731 | ||||||||
\(649\) | 4.68695 | 0.183979 | ||||||||
\(650\) | 30.1236 | 1.18154 | ||||||||
\(651\) | −4.13048 | −0.161886 | ||||||||
\(652\) | −50.1918 | −1.96566 | ||||||||
\(653\) | −14.1153 | −0.552376 | −0.276188 | − | 0.961104i | \(-0.589071\pi\) | ||||
−0.276188 | + | 0.961104i | \(0.589071\pi\) | |||||||
\(654\) | −32.9139 | −1.28703 | ||||||||
\(655\) | −9.18626 | −0.358937 | ||||||||
\(656\) | −10.1795 | −0.397443 | ||||||||
\(657\) | 5.34108 | 0.208375 | ||||||||
\(658\) | −12.1591 | −0.474012 | ||||||||
\(659\) | −1.61937 | −0.0630817 | −0.0315409 | − | 0.999502i | \(-0.510041\pi\) | ||||
−0.0315409 | + | 0.999502i | \(0.510041\pi\) | |||||||
\(660\) | −12.6924 | −0.494051 | ||||||||
\(661\) | 18.0663 | 0.702699 | 0.351350 | − | 0.936244i | \(-0.385723\pi\) | ||||
0.351350 | + | 0.936244i | \(0.385723\pi\) | |||||||
\(662\) | 16.0209 | 0.622669 | ||||||||
\(663\) | 14.0181 | 0.544416 | ||||||||
\(664\) | 26.8549 | 1.04217 | ||||||||
\(665\) | 8.40701 | 0.326010 | ||||||||
\(666\) | 13.7902 | 0.534358 | ||||||||
\(667\) | 31.4582 | 1.21807 | ||||||||
\(668\) | 44.2950 | 1.71382 | ||||||||
\(669\) | −4.94454 | −0.191167 | ||||||||
\(670\) | −14.1529 | −0.546775 | ||||||||
\(671\) | 10.9026 | 0.420892 | ||||||||
\(672\) | −6.60695 | −0.254869 | ||||||||
\(673\) | 27.9142 | 1.07601 | 0.538007 | − | 0.842941i | \(-0.319177\pi\) | ||||
0.538007 | + | 0.842941i | \(0.319177\pi\) | |||||||
\(674\) | 22.0075 | 0.847696 | ||||||||
\(675\) | −3.55029 | −0.136651 | ||||||||
\(676\) | 4.00531 | 0.154050 | ||||||||
\(677\) | −25.2401 | −0.970055 | −0.485028 | − | 0.874499i | \(-0.661190\pi\) | ||||
−0.485028 | + | 0.874499i | \(0.661190\pi\) | |||||||
\(678\) | 42.7827 | 1.64306 | ||||||||
\(679\) | 15.6599 | 0.600971 | ||||||||
\(680\) | 10.2596 | 0.393437 | ||||||||
\(681\) | 27.0946 | 1.03827 | ||||||||
\(682\) | −32.2576 | −1.23521 | ||||||||
\(683\) | 18.4650 | 0.706545 | 0.353272 | − | 0.935521i | \(-0.385069\pi\) | ||||
0.353272 | + | 0.935521i | \(0.385069\pi\) | |||||||
\(684\) | 21.1296 | 0.807909 | ||||||||
\(685\) | −9.81909 | −0.375168 | ||||||||
\(686\) | 2.24191 | 0.0855964 | ||||||||
\(687\) | −14.5531 | −0.555235 | ||||||||
\(688\) | 8.35960 | 0.318707 | ||||||||
\(689\) | 21.7241 | 0.827623 | ||||||||
\(690\) | 10.5647 | 0.402191 | ||||||||
\(691\) | 6.65792 | 0.253279 | 0.126640 | − | 0.991949i | \(-0.459581\pi\) | ||||
0.126640 | + | 0.991949i | \(0.459581\pi\) | |||||||
\(692\) | 25.6881 | 0.976516 | ||||||||
\(693\) | −3.48348 | −0.132326 | ||||||||
\(694\) | −50.3080 | −1.90967 | ||||||||
\(695\) | 1.71619 | 0.0650989 | ||||||||
\(696\) | −18.4911 | −0.700902 | ||||||||
\(697\) | 42.1402 | 1.59617 | ||||||||
\(698\) | −40.6699 | −1.53938 | ||||||||
\(699\) | 8.11619 | 0.306983 | ||||||||
\(700\) | 10.7437 | 0.406073 | ||||||||
\(701\) | −39.3784 | −1.48730 | −0.743650 | − | 0.668569i | \(-0.766907\pi\) | ||||
−0.743650 | + | 0.668569i | \(0.766907\pi\) | |||||||
\(702\) | −8.48483 | −0.320239 | ||||||||
\(703\) | −42.9490 | −1.61985 | ||||||||
\(704\) | −45.3643 | −1.70973 | ||||||||
\(705\) | 6.53019 | 0.245941 | ||||||||
\(706\) | 19.5506 | 0.735795 | ||||||||
\(707\) | 7.53953 | 0.283553 | ||||||||
\(708\) | 4.07162 | 0.153021 | ||||||||
\(709\) | 14.2938 | 0.536813 | 0.268407 | − | 0.963306i | \(-0.413503\pi\) | ||||
0.268407 | + | 0.963306i | \(0.413503\pi\) | |||||||
\(710\) | −26.3826 | −0.990123 | ||||||||
\(711\) | −9.87463 | −0.370327 | ||||||||
\(712\) | −7.31319 | −0.274073 | ||||||||
\(713\) | 16.1659 | 0.605417 | ||||||||
\(714\) | 8.30386 | 0.310764 | ||||||||
\(715\) | −15.8738 | −0.593645 | ||||||||
\(716\) | −66.3723 | −2.48045 | ||||||||
\(717\) | −1.89186 | −0.0706526 | ||||||||
\(718\) | −75.8278 | −2.82987 | ||||||||
\(719\) | 13.8039 | 0.514797 | 0.257398 | − | 0.966305i | \(-0.417135\pi\) | ||||
0.257398 | + | 0.966305i | \(0.417135\pi\) | |||||||
\(720\) | 1.07729 | 0.0401484 | ||||||||
\(721\) | −8.05022 | −0.299806 | ||||||||
\(722\) | −66.7036 | −2.48245 | ||||||||
\(723\) | −8.61286 | −0.320316 | ||||||||
\(724\) | 32.7981 | 1.21893 | ||||||||
\(725\) | −28.5364 | −1.05981 | ||||||||
\(726\) | −2.54372 | −0.0944064 | ||||||||
\(727\) | −13.3120 | −0.493715 | −0.246858 | − | 0.969052i | \(-0.579398\pi\) | ||||
−0.246858 | + | 0.969052i | \(0.579398\pi\) | |||||||
\(728\) | 8.70667 | 0.322691 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.4174 | 0.533612 | ||||||||
\(731\) | −34.6063 | −1.27996 | ||||||||
\(732\) | 9.47128 | 0.350068 | ||||||||
\(733\) | −4.48646 | −0.165711 | −0.0828556 | − | 0.996562i | \(-0.526404\pi\) | ||||
−0.0828556 | + | 0.996562i | \(0.526404\pi\) | |||||||
\(734\) | −4.97472 | −0.183620 | ||||||||
\(735\) | −1.20404 | −0.0444117 | ||||||||
\(736\) | 25.8583 | 0.953149 | ||||||||
\(737\) | −18.2642 | −0.672771 | ||||||||
\(738\) | −25.5065 | −0.938909 | ||||||||
\(739\) | 0.966570 | 0.0355559 | 0.0177779 | − | 0.999842i | \(-0.494341\pi\) | ||||
0.0177779 | + | 0.999842i | \(0.494341\pi\) | |||||||
\(740\) | 22.4121 | 0.823886 | ||||||||
\(741\) | 26.4257 | 0.970772 | ||||||||
\(742\) | 12.8687 | 0.472424 | ||||||||
\(743\) | 4.92768 | 0.180779 | 0.0903895 | − | 0.995906i | \(-0.471189\pi\) | ||||
0.0903895 | + | 0.995906i | \(0.471189\pi\) | |||||||
\(744\) | −9.50228 | −0.348370 | ||||||||
\(745\) | 5.94208 | 0.217701 | ||||||||
\(746\) | −33.5282 | −1.22756 | ||||||||
\(747\) | −11.6734 | −0.427106 | ||||||||
\(748\) | 39.0450 | 1.42763 | ||||||||
\(749\) | −19.3415 | −0.706723 | ||||||||
\(750\) | −23.0802 | −0.842769 | ||||||||
\(751\) | −28.5188 | −1.04067 | −0.520333 | − | 0.853963i | \(-0.674192\pi\) | ||||
−0.520333 | + | 0.853963i | \(0.674192\pi\) | |||||||
\(752\) | 4.85264 | 0.176957 | ||||||||
\(753\) | −15.7496 | −0.573948 | ||||||||
\(754\) | −68.1991 | −2.48366 | ||||||||
\(755\) | −18.5242 | −0.674165 | ||||||||
\(756\) | −3.02615 | −0.110060 | ||||||||
\(757\) | −24.1755 | −0.878672 | −0.439336 | − | 0.898323i | \(-0.644786\pi\) | ||||
−0.439336 | + | 0.898323i | \(0.644786\pi\) | |||||||
\(758\) | 38.7276 | 1.40665 | ||||||||
\(759\) | 13.6336 | 0.494870 | ||||||||
\(760\) | 19.3405 | 0.701555 | ||||||||
\(761\) | 16.0558 | 0.582023 | 0.291011 | − | 0.956720i | \(-0.406008\pi\) | ||||
0.291011 | + | 0.956720i | \(0.406008\pi\) | |||||||
\(762\) | −7.07512 | −0.256305 | ||||||||
\(763\) | −14.6812 | −0.531495 | ||||||||
\(764\) | −3.02615 | −0.109482 | ||||||||
\(765\) | −4.45968 | −0.161240 | ||||||||
\(766\) | 37.0959 | 1.34033 | ||||||||
\(767\) | 5.09217 | 0.183868 | ||||||||
\(768\) | −9.78427 | −0.353060 | ||||||||
\(769\) | 48.8293 | 1.76083 | 0.880414 | − | 0.474205i | \(-0.157265\pi\) | ||||
0.880414 | + | 0.474205i | \(0.157265\pi\) | |||||||
\(770\) | −9.40311 | −0.338865 | ||||||||
\(771\) | 24.8268 | 0.894116 | ||||||||
\(772\) | −1.10061 | −0.0396118 | ||||||||
\(773\) | −17.3983 | −0.625773 | −0.312887 | − | 0.949790i | \(-0.601296\pi\) | ||||
−0.312887 | + | 0.949790i | \(0.601296\pi\) | |||||||
\(774\) | 20.9464 | 0.752904 | ||||||||
\(775\) | −14.6644 | −0.526761 | ||||||||
\(776\) | 36.0259 | 1.29325 | ||||||||
\(777\) | 6.15109 | 0.220669 | ||||||||
\(778\) | −62.2396 | −2.23140 | ||||||||
\(779\) | 79.4392 | 2.84621 | ||||||||
\(780\) | −13.7897 | −0.493752 | ||||||||
\(781\) | −34.0466 | −1.21828 | ||||||||
\(782\) | −32.4996 | −1.16218 | ||||||||
\(783\) | 8.03776 | 0.287246 | ||||||||
\(784\) | −0.894732 | −0.0319547 | ||||||||
\(785\) | −13.7294 | −0.490025 | ||||||||
\(786\) | −17.1047 | −0.610104 | ||||||||
\(787\) | 18.7514 | 0.668417 | 0.334208 | − | 0.942499i | \(-0.391531\pi\) | ||||
0.334208 | + | 0.942499i | \(0.391531\pi\) | |||||||
\(788\) | −60.3600 | −2.15024 | ||||||||
\(789\) | 26.0980 | 0.929115 | ||||||||
\(790\) | −26.6550 | −0.948343 | ||||||||
\(791\) | 19.0832 | 0.678520 | ||||||||
\(792\) | −8.01383 | −0.284759 | ||||||||
\(793\) | 11.8453 | 0.420637 | ||||||||
\(794\) | −21.1859 | −0.751860 | ||||||||
\(795\) | −6.91126 | −0.245117 | ||||||||
\(796\) | 33.7510 | 1.19627 | ||||||||
\(797\) | 5.39559 | 0.191122 | 0.0955608 | − | 0.995424i | \(-0.469536\pi\) | ||||
0.0955608 | + | 0.995424i | \(0.469536\pi\) | |||||||
\(798\) | 15.6538 | 0.554137 | ||||||||
\(799\) | −20.0885 | −0.710679 | ||||||||
\(800\) | −23.4566 | −0.829316 | ||||||||
\(801\) | 3.17892 | 0.112322 | ||||||||
\(802\) | 21.5017 | 0.759250 | ||||||||
\(803\) | 18.6055 | 0.656575 | ||||||||
\(804\) | −15.8664 | −0.559564 | ||||||||
\(805\) | 4.71237 | 0.166089 | ||||||||
\(806\) | −35.0465 | −1.23446 | ||||||||
\(807\) | −21.2558 | −0.748241 | ||||||||
\(808\) | 17.3449 | 0.610190 | ||||||||
\(809\) | −14.3162 | −0.503330 | −0.251665 | − | 0.967814i | \(-0.580978\pi\) | ||||
−0.251665 | + | 0.967814i | \(0.580978\pi\) | |||||||
\(810\) | 2.69935 | 0.0948453 | ||||||||
\(811\) | 50.0702 | 1.75820 | 0.879102 | − | 0.476634i | \(-0.158143\pi\) | ||||
0.879102 | + | 0.476634i | \(0.158143\pi\) | |||||||
\(812\) | −24.3234 | −0.853586 | ||||||||
\(813\) | −14.8459 | −0.520667 | ||||||||
\(814\) | 48.0378 | 1.68372 | ||||||||
\(815\) | 19.9703 | 0.699528 | ||||||||
\(816\) | −3.31402 | −0.116014 | ||||||||
\(817\) | −65.2369 | −2.28235 | ||||||||
\(818\) | 15.0563 | 0.526431 | ||||||||
\(819\) | −3.78465 | −0.132246 | ||||||||
\(820\) | −41.4538 | −1.44763 | ||||||||
\(821\) | −14.5302 | −0.507109 | −0.253554 | − | 0.967321i | \(-0.581600\pi\) | ||||
−0.253554 | + | 0.967321i | \(0.581600\pi\) | |||||||
\(822\) | −18.2830 | −0.637694 | ||||||||
\(823\) | −10.3577 | −0.361047 | −0.180524 | − | 0.983571i | \(-0.557779\pi\) | ||||
−0.180524 | + | 0.983571i | \(0.557779\pi\) | |||||||
\(824\) | −18.5197 | −0.645165 | ||||||||
\(825\) | −12.3674 | −0.430576 | ||||||||
\(826\) | 3.01644 | 0.104955 | ||||||||
\(827\) | 6.80040 | 0.236473 | 0.118237 | − | 0.992985i | \(-0.462276\pi\) | ||||
0.118237 | + | 0.992985i | \(0.462276\pi\) | |||||||
\(828\) | 11.8437 | 0.411598 | ||||||||
\(829\) | −17.0895 | −0.593544 | −0.296772 | − | 0.954948i | \(-0.595910\pi\) | ||||
−0.296772 | + | 0.954948i | \(0.595910\pi\) | |||||||
\(830\) | −31.5104 | −1.09374 | ||||||||
\(831\) | −17.8482 | −0.619148 | ||||||||
\(832\) | −49.2864 | −1.70870 | ||||||||
\(833\) | 3.70393 | 0.128333 | ||||||||
\(834\) | 3.19553 | 0.110652 | ||||||||
\(835\) | −17.6240 | −0.609905 | ||||||||
\(836\) | 73.6044 | 2.54566 | ||||||||
\(837\) | 4.13048 | 0.142770 | ||||||||
\(838\) | −62.1161 | −2.14576 | ||||||||
\(839\) | 43.6093 | 1.50556 | 0.752780 | − | 0.658272i | \(-0.228712\pi\) | ||||
0.752780 | + | 0.658272i | \(0.228712\pi\) | |||||||
\(840\) | −2.76992 | −0.0955714 | ||||||||
\(841\) | 35.6056 | 1.22778 | ||||||||
\(842\) | −56.1899 | −1.93643 | ||||||||
\(843\) | −2.89496 | −0.0997077 | ||||||||
\(844\) | −13.1307 | −0.451979 | ||||||||
\(845\) | −1.59363 | −0.0548225 | ||||||||
\(846\) | 12.1591 | 0.418039 | ||||||||
\(847\) | −1.13462 | −0.0389862 | ||||||||
\(848\) | −5.13582 | −0.176365 | ||||||||
\(849\) | −25.7601 | −0.884085 | ||||||||
\(850\) | 29.4811 | 1.01119 | ||||||||
\(851\) | −24.0741 | −0.825251 | ||||||||
\(852\) | −29.5767 | −1.01328 | ||||||||
\(853\) | −38.9952 | −1.33517 | −0.667585 | − | 0.744534i | \(-0.732672\pi\) | ||||
−0.667585 | + | 0.744534i | \(0.732672\pi\) | |||||||
\(854\) | 7.01675 | 0.240108 | ||||||||
\(855\) | −8.40701 | −0.287514 | ||||||||
\(856\) | −44.4956 | −1.52083 | ||||||||
\(857\) | −26.1287 | −0.892540 | −0.446270 | − | 0.894898i | \(-0.647248\pi\) | ||||
−0.446270 | + | 0.894898i | \(0.647248\pi\) | |||||||
\(858\) | −29.5567 | −1.00905 | ||||||||
\(859\) | −53.4346 | −1.82316 | −0.911582 | − | 0.411118i | \(-0.865138\pi\) | ||||
−0.911582 | + | 0.411118i | \(0.865138\pi\) | |||||||
\(860\) | 34.0426 | 1.16084 | ||||||||
\(861\) | −11.3772 | −0.387733 | ||||||||
\(862\) | 12.6448 | 0.430684 | ||||||||
\(863\) | 17.4117 | 0.592702 | 0.296351 | − | 0.955079i | \(-0.404230\pi\) | ||||
0.296351 | + | 0.955079i | \(0.404230\pi\) | |||||||
\(864\) | 6.60695 | 0.224773 | ||||||||
\(865\) | −10.2208 | −0.347516 | ||||||||
\(866\) | −66.0399 | −2.24413 | ||||||||
\(867\) | −3.28093 | −0.111426 | ||||||||
\(868\) | −12.4994 | −0.424259 | ||||||||
\(869\) | −34.3981 | −1.16687 | ||||||||
\(870\) | 21.6967 | 0.735587 | ||||||||
\(871\) | −19.8433 | −0.672364 | ||||||||
\(872\) | −33.7744 | −1.14375 | ||||||||
\(873\) | −15.6599 | −0.530006 | ||||||||
\(874\) | −61.2656 | −2.07234 | ||||||||
\(875\) | −10.2949 | −0.348031 | ||||||||
\(876\) | 16.1629 | 0.546093 | ||||||||
\(877\) | 18.0988 | 0.611154 | 0.305577 | − | 0.952167i | \(-0.401151\pi\) | ||||
0.305577 | + | 0.952167i | \(0.401151\pi\) | |||||||
\(878\) | −54.5032 | −1.83939 | ||||||||
\(879\) | −26.5108 | −0.894188 | ||||||||
\(880\) | 3.75273 | 0.126504 | ||||||||
\(881\) | −10.9182 | −0.367842 | −0.183921 | − | 0.982941i | \(-0.558879\pi\) | ||||
−0.183921 | + | 0.982941i | \(0.558879\pi\) | |||||||
\(882\) | −2.24191 | −0.0754889 | ||||||||
\(883\) | −54.1923 | −1.82372 | −0.911858 | − | 0.410506i | \(-0.865352\pi\) | ||||
−0.911858 | + | 0.410506i | \(0.865352\pi\) | |||||||
\(884\) | 42.4207 | 1.42676 | ||||||||
\(885\) | −1.62001 | −0.0544561 | ||||||||
\(886\) | −33.8151 | −1.13604 | ||||||||
\(887\) | 25.5060 | 0.856407 | 0.428203 | − | 0.903682i | \(-0.359147\pi\) | ||||
0.428203 | + | 0.903682i | \(0.359147\pi\) | |||||||
\(888\) | 14.1507 | 0.474867 | ||||||||
\(889\) | −3.15585 | −0.105844 | ||||||||
\(890\) | 8.58101 | 0.287636 | ||||||||
\(891\) | 3.48348 | 0.116701 | ||||||||
\(892\) | −14.9629 | −0.500995 | ||||||||
\(893\) | −37.8692 | −1.26724 | ||||||||
\(894\) | 11.0641 | 0.370038 | ||||||||
\(895\) | 26.4081 | 0.882726 | ||||||||
\(896\) | −15.9818 | −0.533914 | ||||||||
\(897\) | 14.8124 | 0.494570 | ||||||||
\(898\) | −73.2213 | −2.44343 | ||||||||
\(899\) | 33.1998 | 1.10728 | ||||||||
\(900\) | −10.7437 | −0.358123 | ||||||||
\(901\) | 21.2608 | 0.708299 | ||||||||
\(902\) | −88.8515 | −2.95843 | ||||||||
\(903\) | 9.34313 | 0.310920 | ||||||||
\(904\) | 43.9013 | 1.46014 | ||||||||
\(905\) | −13.0497 | −0.433786 | ||||||||
\(906\) | −34.4918 | −1.14591 | ||||||||
\(907\) | −31.9202 | −1.05989 | −0.529946 | − | 0.848031i | \(-0.677788\pi\) | ||||
−0.529946 | + | 0.848031i | \(0.677788\pi\) | |||||||
\(908\) | 81.9921 | 2.72100 | ||||||||
\(909\) | −7.53953 | −0.250070 | ||||||||
\(910\) | −10.2161 | −0.338660 | ||||||||
\(911\) | 6.20266 | 0.205503 | 0.102752 | − | 0.994707i | \(-0.467235\pi\) | ||||
0.102752 | + | 0.994707i | \(0.467235\pi\) | |||||||
\(912\) | −6.24732 | −0.206870 | ||||||||
\(913\) | −40.6639 | −1.34578 | ||||||||
\(914\) | −14.9784 | −0.495440 | ||||||||
\(915\) | −3.76842 | −0.124580 | ||||||||
\(916\) | −44.0398 | −1.45512 | ||||||||
\(917\) | −7.62953 | −0.251949 | ||||||||
\(918\) | −8.30386 | −0.274068 | ||||||||
\(919\) | −35.6245 | −1.17514 | −0.587572 | − | 0.809172i | \(-0.699916\pi\) | ||||
−0.587572 | + | 0.809172i | \(0.699916\pi\) | |||||||
\(920\) | 10.8409 | 0.357415 | ||||||||
\(921\) | 8.26367 | 0.272297 | ||||||||
\(922\) | −84.0521 | −2.76811 | ||||||||
\(923\) | −36.9901 | −1.21754 | ||||||||
\(924\) | −10.5415 | −0.346790 | ||||||||
\(925\) | 21.8381 | 0.718034 | ||||||||
\(926\) | 70.0380 | 2.30159 | ||||||||
\(927\) | 8.05022 | 0.264404 | ||||||||
\(928\) | 53.1051 | 1.74326 | ||||||||
\(929\) | 4.68564 | 0.153731 | 0.0768654 | − | 0.997041i | \(-0.475509\pi\) | ||||
0.0768654 | + | 0.997041i | \(0.475509\pi\) | |||||||
\(930\) | 11.1496 | 0.365610 | ||||||||
\(931\) | 6.98234 | 0.228837 | ||||||||
\(932\) | 24.5608 | 0.804515 | ||||||||
\(933\) | 0.313790 | 0.0102730 | ||||||||
\(934\) | 52.0256 | 1.70233 | ||||||||
\(935\) | −15.5352 | −0.508055 | ||||||||
\(936\) | −8.70667 | −0.284587 | ||||||||
\(937\) | 1.16457 | 0.0380449 | 0.0190224 | − | 0.999819i | \(-0.493945\pi\) | ||||
0.0190224 | + | 0.999819i | \(0.493945\pi\) | |||||||
\(938\) | −11.7545 | −0.383799 | ||||||||
\(939\) | −30.6173 | −0.999159 | ||||||||
\(940\) | 19.7613 | 0.644542 | ||||||||
\(941\) | 9.35854 | 0.305080 | 0.152540 | − | 0.988297i | \(-0.451255\pi\) | ||||
0.152540 | + | 0.988297i | \(0.451255\pi\) | |||||||
\(942\) | −25.5640 | −0.832922 | ||||||||
\(943\) | 44.5279 | 1.45003 | ||||||||
\(944\) | −1.20384 | −0.0391818 | ||||||||
\(945\) | 1.20404 | 0.0391674 | ||||||||
\(946\) | 72.9665 | 2.37234 | ||||||||
\(947\) | −32.5280 | −1.05702 | −0.528509 | − | 0.848928i | \(-0.677249\pi\) | ||||
−0.528509 | + | 0.848928i | \(0.677249\pi\) | |||||||
\(948\) | −29.8821 | −0.970524 | ||||||||
\(949\) | 20.2141 | 0.656178 | ||||||||
\(950\) | 55.5753 | 1.80310 | ||||||||
\(951\) | 19.4228 | 0.629828 | ||||||||
\(952\) | 8.52097 | 0.276166 | ||||||||
\(953\) | −25.5277 | −0.826922 | −0.413461 | − | 0.910522i | \(-0.635680\pi\) | ||||
−0.413461 | + | 0.910522i | \(0.635680\pi\) | |||||||
\(954\) | −12.8687 | −0.416639 | ||||||||
\(955\) | 1.20404 | 0.0389618 | ||||||||
\(956\) | −5.72503 | −0.185161 | ||||||||
\(957\) | 27.9994 | 0.905091 | ||||||||
\(958\) | 26.3033 | 0.849821 | ||||||||
\(959\) | −8.15512 | −0.263343 | ||||||||
\(960\) | 15.6799 | 0.506065 | ||||||||
\(961\) | −13.9391 | −0.449649 | ||||||||
\(962\) | 52.1910 | 1.68270 | ||||||||
\(963\) | 19.3415 | 0.623271 | ||||||||
\(964\) | −26.0638 | −0.839458 | ||||||||
\(965\) | 0.437909 | 0.0140968 | ||||||||
\(966\) | 8.77437 | 0.282311 | ||||||||
\(967\) | 24.8781 | 0.800027 | 0.400014 | − | 0.916509i | \(-0.369005\pi\) | ||||
0.400014 | + | 0.916509i | \(0.369005\pi\) | |||||||
\(968\) | −2.61023 | −0.0838960 | ||||||||
\(969\) | 25.8621 | 0.830809 | ||||||||
\(970\) | −42.2714 | −1.35725 | ||||||||
\(971\) | −7.02888 | −0.225568 | −0.112784 | − | 0.993620i | \(-0.535977\pi\) | ||||
−0.112784 | + | 0.993620i | \(0.535977\pi\) | |||||||
\(972\) | 3.02615 | 0.0970637 | ||||||||
\(973\) | 1.42536 | 0.0456950 | ||||||||
\(974\) | −91.0187 | −2.91643 | ||||||||
\(975\) | −13.4366 | −0.430315 | ||||||||
\(976\) | −2.80035 | −0.0896369 | ||||||||
\(977\) | 59.4498 | 1.90197 | 0.950984 | − | 0.309241i | \(-0.100075\pi\) | ||||
0.950984 | + | 0.309241i | \(0.100075\pi\) | |||||||
\(978\) | 37.1844 | 1.18903 | ||||||||
\(979\) | 11.0737 | 0.353918 | ||||||||
\(980\) | −3.64360 | −0.116391 | ||||||||
\(981\) | 14.6812 | 0.468735 | ||||||||
\(982\) | 89.2558 | 2.84827 | ||||||||
\(983\) | −41.6665 | −1.32895 | −0.664477 | − | 0.747309i | \(-0.731346\pi\) | ||||
−0.664477 | + | 0.747309i | \(0.731346\pi\) | |||||||
\(984\) | −26.1734 | −0.834379 | ||||||||
\(985\) | 24.0160 | 0.765212 | ||||||||
\(986\) | −66.7445 | −2.12558 | ||||||||
\(987\) | 5.42356 | 0.172634 | ||||||||
\(988\) | 79.9680 | 2.54412 | ||||||||
\(989\) | −36.5671 | −1.16277 | ||||||||
\(990\) | 9.40311 | 0.298850 | ||||||||
\(991\) | −2.68235 | −0.0852077 | −0.0426038 | − | 0.999092i | \(-0.513565\pi\) | ||||
−0.0426038 | + | 0.999092i | \(0.513565\pi\) | |||||||
\(992\) | 27.2899 | 0.866456 | ||||||||
\(993\) | −7.14609 | −0.226774 | ||||||||
\(994\) | −21.9118 | −0.694999 | ||||||||
\(995\) | −13.4288 | −0.425722 | ||||||||
\(996\) | −35.3253 | −1.11933 | ||||||||
\(997\) | −23.7071 | −0.750811 | −0.375405 | − | 0.926861i | \(-0.622497\pi\) | ||||
−0.375405 | + | 0.926861i | \(0.622497\pi\) | |||||||
\(998\) | −18.1457 | −0.574393 | ||||||||
\(999\) | −6.15109 | −0.194612 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4011.2.a.m.1.4 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.m.1.4 | ✓ | 29 | 1.1 | even | 1 | trivial |